39 research outputs found
Spontaneous formation of domain wall lattices in two spatial dimensions
We show that the process of spontaneous symmetry breaking can trap a field
theoretic system in a highly non-trivial state containing a lattice of domain
walls. In one large compact space dimension, a lattice is inevitably formed. In
two dimensions, the probability of lattice formation depends on the ratio of
sizes L_x, L_y of the spatial dimensions. We find that a lattice can form even
if R=L_y/L_x is of order unity. We numerically determine the number of walls in
the lattice as a function of L_x and L_y.Comment: 6 pages, 6 figures. Background material added and minor corrections
included. Final version to be published in Phys. Rev.
The role of domain wall junctions in Carter's pentahedral model
The role of domain wall junctions in Carter's pentahedral model is
investigated both analytically and numerically. We perform, for the first time,
field theory simulations of such model with various initial conditions. We
confirm that there are very specific realizations of Carter's model
corresponding to square lattice configurations with X-type junctions which
could be stable. However, we show that more realistic realizations, consistent
with causality constraints, do lead to a scaling domain wall network with
Y-type junctions. We determine the network properties and discuss the
corresponding cosmological implications, in particular for dark energy.Comment: 6 pages, 6 figure